The basic objective of the proposed research is to improve the capacity of social scientists to deal in a more rigorous way with the structural aspects of social phenomena as manifested, for example, in sociometry, communication net-works, power structures, and the cognitive structures of idividuals. The research will involve the collaborative efforts of a social psychologist and a mathematician and will consist, in part, in bringing known mathematical results to bear on specific problems in social science and, in part, in solving relevant mathematical problems. The work will be primarily concerned with the branches of mathematics having to do with graphs, digraphs, signed graphs, networks, and matrices. It will concentrate on a variety of unsolved problems confronting social scientists in their research on social networks, cliques, balance theory, and the clustering of elements in cognitive and social structures. An investigation will also be made of the applicability to graph theory of certain concepts employed in euclidean geometry.